Problem: Ashley is 2 times as old as Emily. 24 years ago, Ashley was 8 times as old as Emily. How old is Ashley now?
Explanation: We can use the given information to write down two equations that describe the ages of Ashley and Emily. Let Ashley's current age be $a$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $a = 2e$ 24 years ago, Ashley was $a - 24$ years old, and Emily was $e - 24$ years old. The information in the second sentence can be expressed in the following equation: $a - 24 = 8(e - 24)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = a / 2$ . Substituting this into our second equation, we get: $a - 24 = 8($ $(a / 2)$ $- 24)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $a - 24 = 4 a - 192$ Solving for $a$ , we get: $3 a = 168$ $a = \dfrac{1}{3} \cdot 168 = 56$.